I guess this is a type of fiberboard?

Hi all,

Been a long-time lurker - this is a great forum. But, I decided to register as I've come across something in my house (built in the 1940's) that I'm not sure of, and don't really want to mess with it unless I know I can (or it's safe). I have no idea what types of things can contain asbestos, so I'm treading lightly.

There is a sun room, which looks like was added on after the house was built, that has very thin wood paneling. We started to take off the paneling, only to find this soft type of fiberboard underneath. I've seen some pictures online of various types, but would like some opinions of pictures I took of what is in my home:

Now, I took these in one of the bedrooms - we started to take off wood trim around the closet, and as you can see in the 3rd picture, there is drywall over this same fiberboard, which is then attached to a stud.

So, can I go about just ripping this stuff down, or should I be worried/cautious? As I said, I did take a look online and saw many examples which appear similar, however as I don't know the age of the fiberboard (it's not out of the question that this closet, just like the sun room, were built after the house was originally constructed).